[en] A method has been introduced to derive the all order Bose–Einstein distribution as the solution of the Wigner equation. The process is a perturbative one where the Bose–Einstein distribution has been taken as the unperturbed solution. This solution has been applied to calculate the number density of the bosons at finite temperature. The study may be important to investigate the properties of bosons at finite temperature. This process can also be applied to obtain the all order Fermi distribution. (paper: quantum statistical physics, condensed matter, integrable systems)